If the fourth term of a G.P. is 8 and fifth term is 16, then what is the product of first
8 terms?
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Given : fourth term of a G.P. is 8 and fifth term is 16,
To Find : product of first 8 terms
Solution:
Let say GP is
a , ar , ar² ,............................
fourth term of G.P = ar³ = 8
fifth term of G.P = ar⁴ = 16
=> ar⁴ / ar³ = 16/8
=> r = 2
ar³ = 8
=> a(2)³ = 8
=> a = 1
first 8 terms of GP are
1 , 2¹ , 2² , 2³ , 2⁴ , 2⁵ , 2⁶ 2⁷
Product = 1⁰ x 2¹ x 2² x 2³ x 2⁴ x 2⁵ x 2⁶ x 2⁷
= 1 * 2¹⁺²⁺³⁺⁴⁺⁵⁺⁶⁺⁷
= 1 * 2²⁸
= 2²⁸
= 26,84,35,456
product of first 8 terms = 2²⁸ = 26,84,35,456
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